AbstractThis article deals with a quantification of the instability behavior of the slotted multiuser communication network system ALOHA. In (2) U. Schmid and the author could quantify the expected valueE(Y) of theinstability time Y= max (n: Xn= 0), whereXndenotes the backlog afternslots. Here it is shown thatYis approximately exponentially distributed. Moreover, uniform asymptotic expansions forym=P[Y=m] and for the momentsMm=E(Ym) are given. © 1994 John Wiley&Sons, Inc